This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A151691 #18 Oct 04 2024 20:50:54
%S A151691 1,2,1,2,5,4,1,2,5,4,5,12,13,6,1,2,5,4,5,12,13,6,5,12,13,14,29,38,25,
%T A151691 8,1,2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29,38,25,16,29,
%U A151691 38,41,72,105,88,41,10,1,2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29
%N A151691 G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + x^(2^k)).
%H A151691 David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H A151691 N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%e A151691 From _Omar E. Pol_, Jun 09 2009: (Start)
%e A151691 Triangle begins:
%e A151691 1;
%e A151691 2,1;
%e A151691 2,5,4,1;
%e A151691 2,5,4,5,12,13,6,1;
%e A151691 2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,1;
%e A151691 2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29,38,25,16,29,38,41,72,...
%e A151691 (End)
%Y A151691 For generating functions of the form Product_{k>=c} (1 + a*x^(2^k-1) + b*x^2^k) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694.
%Y A151691 Cf. A151685. See A151703 for another version with a simpler recurrence.
%Y A151691 Cf. A000079. - _Omar E. Pol_, Jun 09 2009
%K A151691 nonn
%O A151691 0,2
%A A151691 _N. J. A. Sloane_, Jun 04 2009